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In a quantum Hall interferometer, the dependence of the signal on source-drain voltage is controlled by details of the edge physics, such as the velocities of edge modes and the interaction between them and with screening layers. Such dependence of the signal has been seen in recent experiments at various integer and fractional filling factors, including $\nu=2$ and $\nu=2/5$, where two edge modes are present. Here we study theoretically the current-voltage curves for various values of the relative edge velocities, interaction strength, and the temperature, in a model containing two edge modes. We consider separate cases in which the inner mode or the outer mode is weakly backscattered at the tunneling contacts. When the inner mode is completely reflected and the outer mode is partially transmitted, we find striking features at very low temperatures related to resonance of excitations of the closed inner channel. Fluctuations in the charge of the closed inner mode, caused by sparse tunneling events, lead to an exponential suppression of the interference visibility at high voltages, in agreement with experiments., Comment: 26 pages, 13 figures, typos fixed and reference updated, published in PRB as an Editors' Suggestion

The search for anyons, quasiparticles with fractional charge and exotic exchange statistics, has inspired decades of condensed matter research. Quantum Hall interferometers enable direct observation of the anyon braiding phase via discrete interference phase jumps when the quasiparticle number changes. Here, we observe the universal anyonic braiding phase in both the $\nu = 1/3$ and $4/3$ fractional quantum Hall states by probing three-state random telegraph noise (RTN) in real-time. We find that the observed RTN stems from anyon quasiparticle number $n$ fluctuations and reconstruct three Aharonov-Bohm oscillation signals phase shifted by $2\pi/3$, corresponding to the three possible interference branches from braiding around $n$ (mod 3) anyons. Hence, we fully characterize the anyon exchange statistics using new methods that can readily extend to non-abelian states., Comment: 19 pages, 11 figures

Josephson junctions enable dissipation-less electrical current through metals and insulators below a critical current. Despite being central to quantum technology based on superconducting quantum bits and fundamental research into self-conjugate quasiparticles, the spatial distribution of super current flow at the junction and its predicted evolution with current bias and external magnetic field remain experimentally elusive. Revealing the hidden current flow, featureless in electrical resistance, helps understanding unconventional phenomena such as the nonreciprocal critical current, i.e., Josephson diode effect. Here we introduce a platform to visualize super current flow at the nanoscale. Utilizing a scanning magnetometer based on nitrogen vacancy centers in diamond, we uncover competing ground states electrically switchable within the zero-resistance regime. The competition results from the superconducting phase re-configuration induced by the Josephson current and kinetic inductance of thin-film superconductors. We further identify a new mechanism for the Josephson diode effect involving the Josephson current induced phase. The nanoscale super current flow emerges as a new experimental observable for elucidating unconventional superconductivity, and optimizing quantum computation and energy-efficient devices.

Electronic interferometers using the chiral, one-dimensional (1D) edge channels of the quantum Hall effect (QHE) can demonstrate a wealth of fundamental phenomena. The recent observation of phase jumps in a Fabry-P\'erot (FP) interferometer revealed anyonic quasiparticle exchange statistics in the fractional QHE. When multiple integer edge channels are involved, FP interferometers have exhibited anomalous Aharonov-Bohm (AB) interference frequency doubling, suggesting putative pairing of electrons into 2e quasiparticles. Here, we use a highly tunable graphene-based QHE FP interferometer to observe the connection between interference phase jumps and AB frequency doubling, unveiling how strong repulsive interaction between edge channels leads to the apparent pairing phenomena. By tuning electron density in-situ from filling factor {\nu}<2 to {\nu}>7, we tune the interaction strength and observe periodic interference phase jumps leading to AB frequency doubling. Our observations demonstrate that the combination of repulsive interaction between the spin-split {\nu}=2 edge channels and charge quantization is sufficient to explain the frequency doubling, through a near-perfect charge screening between the localized and extended edge channels. Our results show that interferometers are sensitive probes of microscopic interactions and enable future experiments studying correlated electrons in 1D channels using our highly tunable platform., Comment: 26 pages, 13 figures

We describe two approximation methods designed to capture the leading behavior of the low-energy tail of the momentum-dependent spectral density $A(\mathbf{k}, E)$ and the tunneling density of states $D(E)$ for an injected particle, such as an electron or an exciton, interacting with a bath of phonons at a non-zero initial temperature $T$, including quantum corrections due to the non-zero frequencies of the relevant phonons. In our imaginary-time-dependent Hartree (ITDH) approximation, we consider a situation where the particle is injected into a specified coherent state of the phonon system, and we show how one can use the ITDH approximation to obtain the correlation function $C(\tau)$ for that initial state. The thermal average $C(\tau)$ is obtained, in principle, by integrating the result over all possible initial phonon coherent states, weighted by a thermal distribution. However, in the low-energy tail, one can obtain a good first approximation by considering only initial states near the one that maximizes the integrand. Our second approximation, the fixed-wave-function (FWF) approximation, assumes that the wave function of the injected particle evolves instantaneously to a wave function which then is independent of time, while the phonon system continues to evolve due to interaction with the particle. We discuss how to invert the Laplace transform and how to obtain $A(\mathbf{k},E)$ as well as $D(E)$ from the imaginary-time analysis. The FWF approximation is used to calculate $D(E)$ for a one-dimensional continuum model of a particle interacting with acoustic phonons, and effects due to the quantum motion of phonons are observed. In the classical phonon limit, the dominant behaviors of both the ITDH and FWF approximations in the low-energy tail reduce to that found in the past for a particle in a random potential with a Gaussian statistical distribution., Comment: Manuscript submitted to Physical Review B for inclusion in the collection honoring Emmanuel Rashba

Over the last decade, there have been considerable efforts to observe non-abelian quasi-particles in novel quantum materials and devices. These efforts are motivated by the goals of demonstrating quantum statistics of quasi-particles beyond those of fermions and bosons and of establishing the underlying science for the creation of topologically protected quantum bits. In this review, we focus on efforts to create topological superconducting phases hosting Majorana zero modes. We consider the lessons learned from existing experimental efforts, which are motivating both improvemensts to current platforms and exploration of new approaches. Although the experimental detection of non-abelian quasi-particles remains challenging, the knowledge gained thus far and the opportunities ahead offer high potential for discovery and advances in this exciting area of quantum physics., Comment: Corrected typos, added published Journal reference, and DOI

By directly altering microscopic interactions, pressure provides a powerful tuning knob for the exploration of condensed phases and geophysical phenomena. The megabar regime represents an exciting frontier, where recent discoveries include novel high-temperature superconductors, as well as structural and valence phase transitions. However, at such high pressures, many conventional measurement techniques fail. Here, we demonstrate the ability to perform local magnetometry inside of a diamond anvil cell with sub-micron spatial resolution at megabar pressures. Our approach utilizes a shallow layer of Nitrogen-Vacancy (NV) color centers implanted directly within the anvil; crucially, we choose a crystal cut compatible with the intrinsic symmetries of the NV center to enable functionality at megabar pressures. We apply our technique to characterize a recently discovered hydride superconductor, CeH$_9$. By performing simultaneous magnetometry and electrical transport measurements, we observe the dual signatures of superconductivity: local diamagnetism characteristic of the Meissner effect and a sharp drop of the resistance to near zero. By locally mapping the Meissner effect and flux trapping, we directly image the geometry of superconducting regions, revealing significant inhomogeneities at the micron scale. Our work brings quantum sensing to the megabar frontier and enables the closed loop optimization of superhydride materials synthesis.

Spin squeezing is a form of entanglement that reshapes the quantum projection noise to improve measurement precision. Here, we provide numerical and analytic evidence for the following conjecture: any Hamiltonian exhibiting finite temperature, easy-plane ferromagnetism can be used to generate scalable spin squeezing, thereby enabling quantum-enhanced sensing. Our conjecture is guided by a connection between the quantum Fisher information of pure states and the spontaneous breaking of a continuous symmetry. We demonstrate that spin-squeezing exhibits a phase diagram with a sharp transition between scalable squeezing and non-squeezing. This transition coincides with the equilibrium phase boundary for XY order at a finite temperature. In the scalable squeezing phase, we predict a sensitivity scaling that lies in between the standard quantum limit and the scaling achieved in all-to-all coupled one-axis twisting models. A corollary of our conjecture is that short-ranged versions of two-axis twisting cannot yield scalable metrological gain. Our results provide insights into the landscape of Hamiltonians that can be used to generate metrologically useful quantum states., Comment: 6 pages, 3 figures + 24 pages, 13 figures

Fabry-P\'{e}rot interferometry has emerged as a tool to probe anyon statistics in the quantum Hall effect. The interference phase is interpreted as a combination of a quantized statistical phase and an Aharonov-Bohm phase, proportional to the device area and the charge of the anyons propagating along the device edge. This interpretation faces two challenges. First, the edge states have a finite width and hence the device area is ill-defined. Second, multiple localized anyons may be present in states that overlap with the edge, and it may not be clear whether a second anyon traveling along the edge will go inside or outside the region with a localized anyon and therefore whether or not it should pick up a statistical phase. We show how one may overcome both challenges. In a case where only one chiral edge mode passes through the constrictions defining the interferometer, as when electrons in a constriction are in a Laughlin state with $\nu=1/(2n+1)$ or the integer state at $\nu=1$, we show that the interference phase can be directly related to the total electron charge contained in the interferometer. This holds for arbitrary electron-electron interactions and holds even if the bulk of the interferometer has a higher electron density than the region of the constrictions. In contrast to the device area or to the number of anyons inside a propagating edge channel, the total charge is well-defined. We examine, at the microscopic level, how the relation between charge and phase is maintained when there is a soft confining potential and disorder near the edge of the interferometer, and we discuss briefly the complications that can occur when multiple chiral modes can pass through the constriction., Comment: 13 pages, 3 figures

We introduce a new variational wavefunction for a quantum Hall bilayer at total filling $\nu = 1$, which is based on $s$-wave BCS pairing between composite-fermion electrons in one layer and composite-fermion holes in the other. We compute the overlap of the optimized trial function with the ground state from exact diagonalization calculations of up to 14 electrons in a spherical geometry, and we find excellent agreement over the entire range of values of the ratio between the layer separation and the magnetic length. The trial wavefunction naturally allows for charge imbalance between the layers and provides important insights into how the physics at large interlayer separations crosses over to that at small separations in a fashion analogous to the BEC-BCS crossover., Comment: 18 pages, 8 figures

Symmetry-broken electronic phases support neutral collective excitations. For example, monolayer graphene in the quantum Hall regime hosts a nearly ideal ferromagnetic phase at filling factor $\nu=1$ that spontaneously breaks spin rotation symmetry. This ferromagnet has been shown to support spin-wave excitations known as magnons which can be generated and detected electrically. While long-distance magnon propagation has been demonstrated via transport measurements, important thermodynamic properties of such magnon populations--including the magnon chemical potential and density--have thus far proven out of reach of experiments. Here, we present local measurements of the electron compressibility under the influence of magnons, which reveal a reduction of the $\nu=1$ gap by up to 20%. Combining these measurements with estimates of the temperature, our analysis reveals that the injected magnons bind to electrons and holes to form skyrmions, and it enables extraction of the free magnon density, magnon chemical potential, and average skyrmion spin. Our methods furnish a novel means of probing the thermodynamic properties of charge-neutral excitations that is applicable to other symmetry-broken electronic phases.

Quasiparticles with fractional charge and fractional statistics are key features of the fractional quantum Hall effect. We discuss in detail the definitions of fractional charge and statistics and the ways in which these properties may be observed. In addition to theoretical foundations, we review the present status of the experiments in the area. We also discuss the notions of non-Abelian statistics and attempts to find experimental evidence for the existence of non-Abelian quasiparticles in certain quantum Hall systems., Comment: Review article; references added

At even-denominator Landau level filling fractions, such as $\nu=1/2$, the ground state, in most cases, has no energy gap, and there is no quantized plateau in the Hall conductance. Nevertheless, the states exhibit non-trivial low-energy phenomena. Open questions concerning the proper description of these systems have attracted renewed attention during the last few years. Issues at $\nu=1/2$ include consequences of particle-hole symmetry, which should be present for a spin-aligned system in the limit where one can neglect mixing between Landau levels. Other issues concern questions of anisotropy and geometry, properties at non-zero temperature, and effects of relatively strong disorder. In cases where one does find a gapped even-denominator quantized Hall state, such as $\nu=5/2$ in GaAs structures, major questions have arisen about the nature of the quantum state, which will be discussed briefly in this chapter. The chapter will also discuss phenomena that can occur in a two-component system near half filling, i.e., when the total filling factor $\nu_{\rm{tot}} $ is close to 1., Comment: Chapter published in "Fractional Quantum Hall Effects: New Developments," edited by B. I. Halperin and J. K. Jain, World Scientific Publishing Co., 2020

In fermionic systems, superconductivity and superfluidity are enabled through the condensation of fermion pairs. The nature of this condensate can be tuned by varying the pairing strength, with weak coupling yielding a BCS-like condensate and strong coupling resulting in a BEC-like process. However, demonstration of this cross-over has remained elusive in electronic systems. Here we study graphene double-layers separated by an atomically thin insulator. Under applied magnetic field, electrons and holes couple across the barrier to form bound magneto-excitons whose pairing strength can be continuously tuned by varying the effective layer separation. Using temperature-dependent Coulomb drag and counter-flow current measurements, we demonstrate the capability to tune the magneto-exciton condensate through the entire weak-coupling to strong-coupling phase diagram. Our results establish magneto-exciton condensates in graphene as a model platform to study the crossover between two Bosonic quantum condensate phases in a solid state system., Comment: 7 pages, 3 figures and supplementary materials

The quest for new functionalities in quantum materials has recently been extended to non-equilibrium states, which are interesting both because they exhibit new physical phenomena and because of their potential for high-speed device applications. Notable advances have been made in the creation of metastable phases and in Floquet engineering under external periodic driving. In the context of non-equilibrium superconductivity, examples have included the generation of transient superconductivity above the thermodynamic transition temperature, the excitation of coherent Higgs mode oscillations, and the optical control of the interlayer phase in cuprates. Here, we propose theoretically a novel non-equilibrium phenomenon, through which a prompt quench from a metal to a transient superconducting state could induce large oscillations of the order parameter amplitude. We argue that this oscillating mode could act as a source of parametric amplification of the incident radiation. We report experimental results on optically driven K$_3$C$_{60}$ that are consistent with these predictions. The effect is found to disappear when the onset of the excitation becomes slower than the Higgs mode period, consistent with the theory proposed here. These results open new possibilities for the use of collective modes in many-body systems to induce non-linear optical effects., Comment: 11 pages, 7 figures

Just over fifty years ago, Pierre Hohenberg developed a rigorous proof of the non-existence of long-range order in a two-dimensional superfluid or superconductor at finite temperatures. The proof was immediately extended by N. D. Mermin and H. Wagner to the Heisenberg ferromagnet and antiferromagnet, and shortly thereafter, by Mermin to prove the absence of translational long-range order in a two-dimensional crystal, whether in quantum or classical mechanics. In this paper, we present an extension of the Hohenberg-Mermin-Wagner theorem to give a rigorous proof of the impossibility of long-range ferromagnetic order in an itinerant electron system without spin-orbit coupling or magnetic dipole interactions. We also comment on some situations where there are compelling arguments that long-range order is impossible but no rigorous proof has been given, as well as situations, such as a magnet with long range interactions, or orientational order in a two-dimensional crystal, where long-range order can occur that breaks a continuous symmetry., Comment: 5 pages, 0 figures. Added reference, and minor corrections. Submitted to the Journal of Statistical Physics, for an issue dedicated to the memory of Pierre Hohenberg

The long-sought Majorana fermion is expected to manifest in a topological-superconductor heterostructure as a zero bias conductance peak (ZBCP). As one promising platform for such heterostructures, we investigate the cleaved surface of the topological semimetal Sb(111) using scanning tunneling microscopy and spectroscopy. Remarkably, we find a robust ZBCP on some terraces of the cleaved surface, although no superconductor is present. Using quasiparticle interference imaging, Landau level spectroscopy and density functional theory, we show that the ZBCP originates from a van Hove singularity pushed up to the Fermi level by a sub-surface stacking fault. Amidst the sprint to stake claims on new Majorana fermion systems, our finding highlights the importance of using a local probe together with detailed modeling to check thoroughly for crystal imperfections that may give rise to a trivial ZBCP unrelated to Majorana physics., Comment: 10 pages, 8 figures

Topological superconductors can support localized Majorana states at their boundaries. These quasi-particle excitations have non-Abelian statistics that can be used to encode and manipulate quantum information in a topologically protected manner. While signatures of Majorana bound states have been observed in one-dimensional systems, there is an ongoing effort to find alternative platforms that do not require fine-tuning of parameters and can be easily scalable to large numbers of states. Here we present a novel experimental approach towards a two-dimensional architecture. Using a Josephson junction made of HgTe quantum well coupled to thin-film aluminum, we are able to tune between a trivial and a topological superconducting state by controlling the phase difference $\phi$ across the junction and applying an in-plane magnetic field. We determine the topological state of the induced superconductor by measuring the tunneling conductance at the edge of the junction. At low magnetic fields, we observe a minimum in the tunneling spectra near zero bias, consistent with a trivial superconductor. However, as the magnetic field increases, the tunneling conductance develops a zero-bias peak which persists over a range of $\phi$ that expands systematically with increasing magnetic fields. Our observations are consistent with theoretical predictions for this system and with full quantum mechanical numerical simulations performed on model systems with similar dimensions and parameters. Our work establishes this system as a promising platform for realizing topological superconductivity and for creating and manipulating Majorana modes and will therefore open new avenues for probing topological superconducting phases in two-dimensional systems., Comment: Supplementary contains resized figures. Original files are available upon request

The study of exotic one-dimensional states, particularly those at the edges of topological materials, demand new experimental probes that can access the interplay between charge and spin degrees of freedom. One potential approach is to use a single spin probe, such as a Nitrogen Vacancy center in diamond, which has recently emerged as a versatile tool to probe nanoscale systems in a non-invasive fashion. Here we present a theory describing how noise magnetometry with spin probes can directly address several questions that have emerged in experimental studies of 1D systems, including those in topological materials. We show that by controlling the spin degree of freedom of the probe, it is possible to measure locally and independently local charge and spin correlations of 1D systems. Visualization of 1D edge states, as well as sampling correlations with wavevector resolution can be achieved by tuning the probe-to-sample distance. Furthermore, temperature-dependent measurements of magnetic noise can clearly delineate the dominant scattering mechanism (impurities vs. interactions) -- this is of particular relevance to quantum spin Hall measurements where conductance quantization is not perfect. The possibility to probe both charge and spin excitations in a wide range of length scales opens new pathways to bridging the large gap between atomic scale resolution of scanning probes and global transport measurements., Comment: 14+4 pages, 5 figures

Spin waves are collective excitations of magnetic systems. An attractive setting for studying long-lived spin-wave physics is the quantum Hall (QH) ferromagnet, which forms spontaneously in clean two-dimensional electron systems at low temperature and in a perpendicular magnetic field. We used out-of-equilibrium occupation of QH edge channels in graphene to excite and detect spin waves in magnetically ordered QH states. Our experiments provide direct evidence for long distance spin wave propagation through different ferromagnetic phases in the N=0 Landau level, as well as across the insulating canted antiferromagnetic phase. Our results will enable experimental investigation of the fundamental magnetic properties of these exotic two-dimensional electron systems.

Although numerical studies modeling the quantum hall effect at filling fraction $5/2$ predict either the Pfaffian (Pf) or its particle hole conjugate, the anti-Pfaffian (aPf) state, recent experiments appear to favor a quantized thermal hall conductivity with quantum number $K=5/2$ , rather than the value $K=7/2$ or $K=3/2$ expected for the Pf or aPF state, respectively. While a particle hole symmetric topological order (the PH-Pfaffian) would be consistent with the experiments, this state is believed to be energetically unfavorable in a homogenous system. Here we study the effects of disorder that are assumed to locally nucleate domains of Pf and aPf. When the disorder is relatively weak and the size of domains is relatively large, we find that when the electrical Hall conductance is on the quantized plateau with $\sigma_{xy} = (5/2)(e^2/h)$, the value of $K$ can be only 7/2 or 3/2, with a possible first-order-like transition between them as the magnetic field is varied. However, for sufficiently strong disorder an intermediate state might appear, which we analyze within a network model of the domain walls. Predominantly, we find a thermal metal phase, where $K$ varies continuously and the longitudinal thermal conductivity is non-zero, while the electrical Hall conductivity remains quantized at $(5/2)e^2/h$. However, in a restricted parameter range we find a thermal insulator with $K=5/2$, a disorder stabilized phase which is adiabatically connected to the PH-Pfaffian. We discuss a possible scenario to rationalize these special values of parameters., Comment: Slightly updated version with additional references, 12 pages + references, 9 figures

In the half-filled zero-energy Landau level of bilayer graphene, competing phases with spontaneously broken symmetries and an intriguing quantum critical behavior have been predicted. Here we investigate signatures of these broken-symmetry phases in thermal transport measurements. To this end we calculate the spectrum of spin and valley waves in the $\nu=0$ quantum Hall state of bilayer graphene. The presence of Goldstone modes enables heat transport even at low temperatures, which can serve as compelling evidence for spontaneous symmetry breaking. By varying external electric and magnetic fields it is possible to determine the nature of the symmetry breaking and temperature-dependent measurements may yield additional information about gapped modes., Comment: 5 pages, 3 figures, plus supplementary material

Confined to a two-dimensional plane, electrons in a strong magnetic field travel along the edge in one-dimensional quantum Hall channels that are protected against backscattering. These channels can be used as solid-state analogues of monochromatic beams of light, providing a unique platform for studying electron interference. Electron interferometry is regarded as one of the most promising routes for studying fractional and non-Abelian statistics and quantum entanglement via two-particle interference. However, creating an edge-channel interferometer in which electron-electron interactions play an important role requires a clean system and long phase coherence lengths. Here we realize electronic Mach-Zehnder interferometers with record visibilities of up to 98% using spin- and valley-polarized edge channels that co-propagate along a PN junction in graphene. We find that inter-channel scattering between same-spin edge channels along the physical graphene edge can be used to form beamsplitters, while the absence of inter-channel scattering along gate-defined interfaces can be used to form isolated interferometer arms. Surprisingly, our interferometer is robust to dephasing effects at energies an order of magnitude larger than observed in pioneering experiments on GaAs/AlGaAs quantum wells. Our results shed light on the nature of edge-channel equilibration and open up new possibilities for studying exotic electron statistics and quantum phenomena., Comment: 18 pages, 11 figures

We study spinless electrons in a single channel quantum wire interacting through attractive interaction, and the quantum Hall states that may be constructed by an array of such wires. For a single wire the electrons may form two phases, the Luttinger liquid and the strongly paired phase. The Luttinger liquid is gapless to one- and two-electron excitations, while the strongly paired state is gapped to the former and gapless to the latter. In contrast to the case in which the wire is proximity-coupled to an external superconductor, for an isolated wire there is no separate phase of a topological, weakly paired, superconductor. Rather, this phase is adiabatically connected to the Luttinger liquid phase. The properties of the one dimensional topological superconductor emerge when the number of channels in the wire becomes large. The quantum Hall states that may be formed by an array of single-channel wires depend on the Landau level filling factors. For odd-denominator fillings $\nu=1/(2n+1)$, wires at the Luttinger phase form Laughlin states while wires in the strongly paired phase form bosonic fractional quantum Hall state of strongly-bound pairs at a filling of $1/(8n+4)$. The transition between the two is of the universality class of Ising transitions in three dimensions. For even-denominator fractions $\nu=1/2n$ the two single-wire phases translate into four quantum Hall states. Two of those states are bosonic fractional quantum Hall states of weakly- and strongly- bound pairs of electrons. The other two are non-Abelian quantum Hall states, which originate from coupling wires close to their critical point. One of these non-Abelian states is the Moore-Read state. The transition between all these states are of the universality class of Majorana transitions. We point out some of the properties that characterize the different phases and the phase transitions., Comment: 16 pages

It is well known that there is a particle-hole symmetry for spin-polarized electrons with two-body interactions in a partially filled Landau level, which becomes exact in the limit where the cyclotron energy is large compared to the interaction strength, so one can ignore mixing between Landau levels. This symmetry is explicit in the description of a half-filled Landau level recently introduced by D. T. Son, using Dirac fermions, but it was thought to be absent in the older fermion-Chern- Simons approach, developed by Halperin, Lee, and Read and subsequent authors. We show here, however, that when properly evaluated, the Halperin, Lee, Read (HLR) theory gives results for long-wavelength low-energy physical properties, including the Hall conductance in the presence of impurities and the positions of minima in the magnetoroton spectra for fractional quantized Hall states close to half-filling, that are identical to predictions of the Dirac formulation. In fact, the HLR theory predicts an emergent particle-hole symmetry near half filling, even when the cyclotron energy is finite., Comment: 21 pages, 1 figure, new version accepted by Phys. Rev. X

We consider a two-dimensional electron gas with strong spin-orbit coupling contacted by two superconducting leads, forming a Josephson junction. We show that in the presence of an in-plane Zeeman field the quasi-one-dimensional region between the two superconductors can support a topological superconducting phase hosting Majorana bound states at its ends. We study the phase diagram of the system as a function of the Zeeman field and the phase difference between the two superconductors (treated as an externally controlled parameter). Remarkably, at a phase difference of $\pi$, the topological phase is obtained for almost any value of the Zeeman field and chemical potential. In a setup where the phase is not controlled externally, we find that the system undergoes a first-order topological phase transition when the Zeeman field is varied. At the transition, the phase difference in the ground state changes abruptly from a value close to zero, at which the system is trivial, to a value close to $\pi$, at which the system is topological. The critical current through the junction exhibits a sharp minimum at the critical Zeeman field, and is therefore a natural diagnostic of the transition. We point out that in presence of a symmetry under a modified mirror reflection followed by time reversal, the system belongs to a higher symmetry class and the phase diagram as a function of the phase difference and the Zeeman field becomes richer.

We present experimental data and associated theory for correlations in a series of experiments involving repeated Landau-Zener sweeps through the crossing point of a singlet state and a spin aligned triplet state in a GaAs double quantum dot containing two conduction electrons, which are loaded in the singlet state before each sweep, and the final spin is recorded after each sweep. The experiments reported here measure correlations on time scales from 4 $\mu$s to 2 ms. When the magnetic field is aligned in a direction such that spin-orbit coupling cannot cause spin flips, the correlation spectrum has prominent peaks centered at zero frequency and at the differences of the Larmor frequencies of the nuclei, on top of a frequency-independent background. When the spin-orbit field is relevant, there are additional peaks, centered at the frequencies of the individual species. A theoretical model which neglects the effects of high-frequency charge noise correctly predicts the positions of the observed peaks, and gives a reasonably accurate prediction of the size of the frequency-independent background, but gives peak areas that are larger than the observed areas by a factor of two or more. The observed peak widths are roughly consistent with predictions based on nuclear dephasing times of the order of 60 $\mu$s. However, there is extra weight at the lowest observed frequencies, which suggests the existence of residual correlations on the scale of 2 ms. We speculate on the source of these discrepancies., Comment: 20 pages, 5 figures, 2 tables

Excitons are pairs of electrons and holes bound together by the Coulomb interaction. At low temperatures, excitons can form a Bose-Einstein condensate (BEC), enabling macroscopic phase coherence and superfluidity. An electronic double layer (EDL), in which two parallel conducting layers are separated by an insulator, is an ideal platform to realize a stable exciton BEC. In an EDL under strong magnetic fields, electron-like and hole-like quasi-particles from partially filled Landau levels (LLs) bind into excitons and condense. However, in semiconducting double quantum wells, this magnetic-field-induced exciton BEC has been observed only in sub-Kelvin temperatures due to the relatively strong dielectric screening and large separation of the EDL. Here we report exciton condensation in bilayer graphene EDL separated by a few atomic layers of hexagonal boron nitride (hBN). Driving current in one graphene layer generates a quantized Hall voltage in the other layer, signifying coherent superfluid exciton transport. Owing to the strong Coulomb coupling across the atomically thin dielectric, we find that quantum Hall drag in graphene appears at a temperature an order of magnitude higher than previously observed in GaAs EDL. The wide-range tunability of densities and displacement fields enables exploration of a rich phase diagram of BEC across Landau levels with different filling factors and internal quantum degrees of freedom. The observed robust exciton superfluidity opens up opportunities to investigate various quantum phases of the exciton BEC and design novel electronic devices based on dissipationless transport., Comment: 12 pages, 3 figures and supplementary information

We study quantum Hall interferometers in which the interference loop encircles a quantum anti-dot. We base our study on thermodynamic considerations, which we believe reflect the essential aspects of interference transport phenomena. We find that similar to the more conventional Fabry-Perot quantum Hall interferometers, in which the interference loop forms a quantum dot, the anti-dot interferometer is affected by the electro-static Coulomb interaction between the edge modes defining the loop. We show that in the Aharonov-Bohm regime, in which effects of fractional statistics should be visible, is easier to access in interferometers based on anti-dots than in those based on dots. We discuss the relevance of our results to recent measurements on anti-dots interferometers., Comment: 3 figures

Fermions and bosons are fundamental realizations of exchange statistics, which governs the probability for two particles being close to each other spatially. Anyons in the fractional quantum Hall effect are an example for exchange statistics intermediate between bosons and fermions. We analyze a mesoscopic setup in which two dilute beams of anyons collide with each other, and relate the correlations of current fluctuations to the probability of particles excluding each other spatially. While current correlations for fermions vanish, negative correlations for anyons are a clear signature of a reduced spatial exclusion as compared to fermions., Comment: 7 pages, 3 figures

Conventional $s$-wave superconductivity is understood to arise from singlet pairing of electrons with opposite Fermi momenta, forming Cooper pairs whose net momentum is zero [1]. Several recent studies have focused on structures where such conventional $s$-wave superconductors are coupled to systems with an unusual configuration of electronic spin and momentum at the Fermi surface. Under these conditions, the nature of the paired state can be modified and the system may even undergo a topological phase transition [2, 3]. Here we present measurements and theoretical calculations of several HgTe quantum wells coupled to either aluminum or niobium superconductors and subject to a magnetic field in the plane of the quantum well. By studying the oscillatory response of Josephson interference to the magnitude of the in-plane magnetic field, we find that the induced pairing within the quantum well is spatially varying. Cooper pairs acquire a tunable momentum that grows with magnetic field strength, directly reflecting the response of the spin-dependent Fermi surfaces to the in-plane magnetic field. In addition, in the regime of high electron density, nodes in the induced superconductivity evolve with the electron density in agreement with our model based on the Hamiltonian of Bernevig, Hughes, and Zhang [4]. This agreement allows us to quantitatively extract the value of $\tilde{g}/v_{F}$, where $\tilde{g}$ is the effective g-factor and $v_{F}$ is the Fermi velocity. However, at low density our measurements do not agree with our model in detail. Our new understanding of the interplay between spin physics and superconductivity introduces a way to spatially engineer the order parameter, as well as a general framework within which to investigate electronic spin texture at the Fermi surface of materials.

A proposal to detect the purported canted antiferromagnet order for the $\nu=0$ quantum Hall state of graphene based on a two-terminal spin transport setup is theoretically discussed. In the presence of a magnetic field normal to the graphene plane, a dynamic and inhomogeneous texture of the N\'eel vector lying within the plane should mediate (nearly dissipationless) superfluid transport of spin angular momentum polarized along the $z$ axis, which could serve as a strong support for the canted antiferromagnet scenario. Spin injection and detection can be achieved by coupling two spin-polarized edge channels of the $|\nu|=2$ quantum Hall state on two opposite ends of the $\nu=0$ region. A simple kinetic theory and Onsager reciprocity are invoked to model the spin injection and detection processes, and the transport of spin through the antiferromagnet is accounted for using the Landau-Lifshitz-Gilbert phenomenology., Comment: 5 pages; 5 figures

We investigate capacitively coupled two-qubit quantum gates based on quantum dots. For exchange-only coded qubits electron spin $S$ and its projection $S_z$ are exact quantum numbers. Capacitive coupling between qubits, as distinct from interqubit exchange, preserves these quantum numbers. We prove, both analytically and numerically, that conservation of the spins of individual qubits has dramatic effect on performance of two-qubit gates. By varying the level splittings of individual qubits, $J_a$ and $J_b$, and the interqubit coupling time $t$, we can find an infinite number of triples $(J_a, J_b, t)$ for which the two-qubit entanglement, in combination with appropriate single-qubit rotations, can produce an exact CNOT gate. This statement is true for practically arbitrary magnitude and form of capacitive interqubit coupling. Our findings promise a large decrease in the number of nonlocal (two-qubit) operations in quantum circuits., Comment: 11 pages, 4 figures, Added 2 references

The central-spin problem, in which an electron spin interacts with a nuclear spin bath, is a widely studied model of quantum decoherence. Dynamic nuclear polarization (DNP) occurs in central spin systems when electronic angular momentum is transferred to nuclear spins and is exploited in spin-based quantum information processing for coherent electron and nuclear spin control. However, the mechanisms limiting DNP remain only partially understood. Here, we show that spin-orbit coupling quenches DNP in a GaAs double quantum dot, even though spin-orbit coupling in GaAs is weak. Using Landau-Zener sweeps, we measure the dependence of the electron spin-flip probability on the strength and direction of in-plane magnetic field, allowing us to distinguish effects of the spin-orbit and hyperfine interactions. To confirm our interpretation, we measure high-bandwidth correlations in the electron spin-flip probability and attain results consistent with a significant spin-orbit contribution. We observe that DNP is quenched when the spin-orbit component exceeds the hyperfine, in agreement with a theoretical model. Our results shed new light on the surprising competition between the spin-orbit and hyperfine interactions in central-spin systems., Comment: 5+12 pages, 9 figures

We consider an annular superconductor-insulator-superconductor Josephson-junction, with the insulator being a double layer of electron and holes at Abelian fractional quantum Hall states of identical fillings. When the two superconductors gap out the edge modes, the system has a topological ground state degeneracy in the thermodynamic limit akin to the fractional quantum Hall degeneracy on a torus. In the quasi-one-dimensional limit, where the width of the insulator becomes small, the ground state energies are split. We discuss several implications of the topological degeneracy that survive the crossover to the quasi-one-dimensional limit. In particular, the Josephson effect shows a $2\pi d$-periodicity, where $d$ is the ground state degeneracy in the 2 dimensional limit. We find that at special values of the relative phase between the two superconductors there are protected crossing points in which the degeneracy is not completely lifted. These features occur also if the insulator is a time-reversal-invariant fractional topological insulator. We describe the latter using a construction based on coupled wires. Furthermore, when the superconductors are replaced by systems with an appropriate magnetic order that gap the edges via a spin-flipping backscattering, the Josephson effect is replaced by a spin Josephson effect.

The electron number-parity of the ground state of a semiconductor narowire proximity-coupled to a bulk superconductor can alternate between the quantised values $\pm 1$ if parameters such as the wire length $L$, the chemical potential $\mu$ or the magnetic field $B$ are varied inside the topological superconductor phase. % The parity jumps, which may be interpreted as changes in the occupancy of the fermion state formed from the pair of Majorana modes at opposite ends of the wire, are accompanied by jumps $\delta N$ in the charge of the nanowire, whose values decrease exponentially with the wire length. % We study theoretically the dependence of $\delta N$ on system parameters, and compare the locations in the $\mu$-$B$ plane of parity jumps when the nanowire is or is not proximity-coupled to a bulk superconductor. % We show that, despite the fact that the wave functions of the Majorana modes are localised near the two ends of the wire, the charge-density jumps have spatial distributions that are essentially uniform along the wire length, being proportional to the product of the two Majorana wave functions. % We explain how charge measurements, say by an external single-electron transistor, could reveal these effects. % Whereas existing experimental methods require direct contact to the wire for tunneling measurements, charge sensing avoids this issue and provides an orthogonal measurement to confirm recent experimental developments. % Furthermore, by comparing density of states measurements which show Majorana features at the wire ends with the uniformly-distributed charge measurements, one can rule out alternative explanations for earlier results. % We shed light on a new parameter regime for these wire-superconductor hybrid systems, and propose a related experiment to measure spin density.

We theoretically study transport in two-dimensional semimetals. Typically, electron and hole puddles emerge in the transport layer of these systems due to smooth fluctuations in the potential. We calculate the electric response of the electron-hole liquid subject to zero and finite perpendicular magnetic fields using an effective medium approximation and a complimentary mapping on resistor networks. In the presence of smooth disorder and in the limit of weak electron-hole recombination rate, we find for small but finite overlap of the electron and hole bands an abrupt upturn in resistivity when lowering the temperature but no divergence at zero temperature. We discuss how this behavior is relevant for several experimental realizations and introduce a simple physical explanation for this effect., Comment: 5 pages, 4 figures, plus supplemental material. V2: minor clarifications and an additional reference. V3: as published

A theoretical proposal for realizing and detecting spin supercurrent in an isotropic antiferromagnetic insulator is reported. Superfluid spin transport is achieved by inserting the antiferromagnet between two metallic reservoirs and establishing a spin accumulation in one reservoir such that a spin bias is applied across the magnet. We consider a class of bipartite antiferromagnets with Neel ground states, and temperatures well below the ordering temperature, where spin transport is mediated essentially by the condensate. Landau-Lifshitz and magneto-circuit theories are used to directly relate spin current in different parts of the heterostructure to the spin-mixing conductances characterizing the antiferromagnet|metal interfaces and the antiferromagnet bulk damping parameters, quantities all obtainable from experiments. We study the efficiency of spin angular-momentum transfer at an antiferromagnet|metal interface by developing a microscopic scattering theory for the interface and extracting the spin-mixing conductance for a simple model. Within the model, a quantitative comparison between the spin-mixing conductances obtained for the antiferromagnet|metal and ferromagnet|metal interfaces is made., Comment: 10 pages, 4 figures

The nature of fractional quantum Hall (FQH) states is determined by the interplay between the Coulomb interaction and the symmetries of the system. The unique combination of spin, valley, and orbital degeneracies in bilayer graphene is predicted to produce novel and tunable FQH ground states. Here we present local electronic compressibility measurements of the FQH effect in the lowest Landau level of bilayer graphene. We observe incompressible FQH states at filling factors v = 2p + 2/3 with hints of additional states appearing at v = 2p + 3/5, where p = -2,-1, 0, and 1. This sequence of states breaks particle-hole symmetry and instead obeys a v --> v + 2 symmetry, which highlights the importance of the orbital degeneracy for many-body states in bilayer graphene.

We consider the dynamic nuclear spin polarization (DNP) using two electrons in a double quantum dot in presence of external magnetic field and spin-orbit interaction, in various schemes of periodically repeated sweeps through the S-T+ avoided crossing. By treating the problem semi-classically, we find that generally the DNP have two distinct contributions - a geometrical polarization and a dynamic polarization, which have different dependence on the control parameters such as the sweep rates and waiting times in each period. Both terms show non-trivial dependence on those control parameter. We find that even for small spin-orbit term, the dynamical polarization dominates the DNP in presence of a long waiting period near the S-T+ avoided crossing, of the order of the nuclear Larmor precession periods. A detailed numerical analysis of a specific control regime can explain the oscillations observed by Foletti et.~al.~in arXiv:0801.3613., Comment: 22 pages, 6 figures

Inspired by creation of a fast exchange-only qubit (Medford et al., Phys. Rev. Lett., 111, 050501 (2013)), we develop a theory describing the nonlinear dynamics of two such qubits that are capacitively coupled, when one of them is driven resonantly at a frequency equal to its level splitting. We include conditions of strong driving, where the Rabi frequency is a significant fraction of the level splitting, and we consider situations where the splitting for the second qubit may be the same or different than the first. We demonstrate that coupling between qubits can be detected by reading the response of the second qubit, even when the coupling between them is only of about $1\%$ of their level splittings, and calculate entanglement between qubits. Patterns of nonlinear dynamics of coupled qubits and their entanglement are strongly dependent on the geometry of the system, and the specific mechanism of inter-qubit coupling deeply influences dynamics of both qubits. In particular, we describe the development of irregular dynamics in a two-qubit system, explore approaches for inhibiting it, and demonstrate existence of an optimal range of coupling strength maintaining stability during the operational time., Comment: 11 pages, 6 figures; One additional figure with changes to the text about the results. Additional references included

Experiments on the fractional quantized Hall effect in the zeroth Landau level of graphene have revealed some striking differences between filling factors in the ranges 0<|\nu|<1 and 1<|\nu|<2. We argue that these differences can be largely understood as a consequence of the effects of terms in the Hamiltonian which break SU(2) valley symmetry, which we find to be important for |\nu|<1 but negligible for |\nu| >1. The effective absence of valley anisotropy for |\nu|>1 means that states with odd numerator, e.g. |\nu|=5/3 or 7/5 can accommodate charged excitations in the form of large valley skyrmions, which have a low energy cost, and may be easily induced by coupling to impurities. The absence of observed quantum Hall states at these fractions is likely due to the effects of valley skyrmions. For |\nu|<1, the anisotropy terms favor phases in which electrons occupy states with opposite spins, similar to the antiferromagnetic state previously hypothesized to be the ground state at \nu=0. The anisotropy and Zeeman energies suppress large-area skyrmions, so that quantized Hall states can be observable at a set of fractions similar to those in GaAs two-dimensional electron systems. In a perpendicular magnetic field B, the competition between the Coulomb energy, which varies as B^{1/2}, and the Zeeman energy, which varies as B, can explain the observation of apparent phase transitions as a function of B for fixed \nu, as transitions between states with different degrees of spin polarization. In addition to an analysis of various fractional states, and an examination of the effects of disorder on valley skyrmions, we present new experimental data for the energy gaps at integer fillings \nu=0 and \nu= -1, as a function of magnetic field, and we examine the possibility that valley-skyrmions may account for the smaller energy gaps observed at \nu= -1., Comment: 19 pages, 1 figure